Geometric implicit neural representations for signed distance functions

TL;DR

This paper reviews geometric implicit neural representations (INRs) for signed distance functions, emphasizing their use in 3D surface reconstruction from point clouds and images, and discusses key methodological advances.

Contribution

It provides a comprehensive survey of geometric INRs for SDFs, detailing loss functions, sampling schemes, and their role in improving 3D surface reconstruction.

Findings

Enhanced surface reconstruction accuracy with geometric INRs

Incorporation of differential geometry tools improves SDF approximation

Regularization terms ensure global properties like unit gradient in SDFs

Abstract

\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating \textit{signed distance functions} (SDFs) for surface scenes, using either oriented point clouds or a set of posed images. We refer to neural SDFs that incorporate differential geometry tools, such as normals and curvatures, in their loss functions as \textit{geometric} INRs. The key idea behind this 3D reconstruction approach is to include additional \textit{regularization} terms in the loss function, ensuring that the INR satisfies certain global properties that the function should hold -- such as having unit gradient in the case of SDFs. We explore key methodological components, including the definition of INR, the construction of geometric loss functions, and sampling schemes from a differential geometry perspective. Our review highlights the significant advancements enabled by geometric INRs in surface reconstruction from oriented point clouds and posed images.